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Questions tagged [transfer-function]

Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.

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300 views

Implementing headphone transfer function (HPTF)

This document on HRTFs, A Spherical Far Field HRIR/HRTF Compilation, of the Neumann KU 100, talks about headphone compensation filters. Searching Google returns http://www.ak.tu-berlin.de/fileadmin/...
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Is any time-domain vector stored on a digital machine always intrinsically causal? [closed]

Reading up on causality, I understand the mathematical definition, in so far as that a causal system, is one where the output depends only on the current time, and possibly the past time, but never ...
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Inverse system in Simulink

I have the following inverse system $$G(s)= s^2 + 2s + 3$$ How do I implement it in Simulink? Note that the transfer function is only accepted if and only if the order of the numerator is less than ...
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1answer
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Build discrete IIR from a transfer function which is not in terms of $s$

Firstly I should state that my maths knowledge is limited. I'm currently designing an acoustics modelling application which uses a rectilinear FDTD grid for modelling pressure variations - but I've ...
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7answers
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Why more poles than zeroes?

I read that an "improper system" "has more zeros than poles; it is not causal, cannot be implemented, has a strictly proper inverse and has infinite high-frequency gain." Does causality fail due to ...
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Converting mel spectrogram to spectrogram

I have a set of songs for which I extracted the STFT (Short-Time Fourier Transform) and used the magnitude spectrum $|S|$ to calculate the mel spectrogram by using a mel filterbank matrix $M$, so $X=\...
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3answers
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How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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4answers
796 views

Transfer function between voltage and decibel output for in-ear headphones

What would be a decent formula for approximating the connection between voltage and decibel output for a typical set of unpowered in-ear headphones? I'm generating sine waves from the computer: an ...
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1answer
535 views

z-space replaces multiplication with convolution and frequency eigenvectors

The frequency domain is allegedly preferred because it replaces convolution of complexity $n^2$ with a diagonal matrix multiplication. Yet, I see that in z-domain we have multiplication of polynomials,...
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1answer
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Cascade Transfer Function; Odd or Even Transfer Function

suppose we have a cascade realization of a transfer function of a higher order. What difference does it make if the order of the transfer function is an Even or an Odd number?
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1answer
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Transfer Function from input to node [closed]

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node:
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2answers
3k views

Finding the frequency response of a filter defined as a Z-domain transfer function

I am software engineer studying DSP on my own. I came across this question in a graduate textbook and am not sure how to proceed. ...
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1answer
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Why is a feedback loop not represented by the least order transfer function?

I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(z)C(z)}$. $$H(z) = h\quad \text{and} \quad C(z) = \frac{K}{z-\alpha}.$$ If I manually calculate the transfer function, I get: $$L(z) =...
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0answers
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Digital control: Exercise solution

Can you help me (show me how) to solve the following exercise? For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
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3answers
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Fill matlab “ellip” function through transfer function magnitude response

The matlab "ellip" function can be used to design the unquantised coefficient set. From matlab website: $ [b,a]=ellip(n,Rp,Rs,Wp) , $ n: order of filter Wp: normalized passband edge ...
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2answers
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Can I determine a system's $z$-domain transfer function from its pole-zero plot?

Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
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1answer
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How to show that this filter is a HP filter

i got a system with transfer function given by: $$H(\omega)=1-e^{-j\omega}$$ I already plot it, and that seems to be a periodic function with $H(0)=0$, $H(\pi)=2$, , is that enough to show that this ...
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1answer
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Determine the type of filter from the transfer function

i got that system $x_n \to x_n-x_{n-1}$, so $h_n=[.....,0,1,-1,0,...]$, with $h_0=1$ and $h_1=-1$, so the transfer function given by: $$\sum_{i=-\infty}^{\infty} h_ne^{-jwn} = h_0e^{-jw(0)}+h_1e^{-jw(...
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1answer
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If exponentials are eigenfunctions, where does the transient term come from?

Here you can see that the transfer function applied to a cosine input will give you a sinusoid and a transient term: $$ x(t) = \underbrace{(x(0) + x'(0))(2 e^{-t} - e^{-2t}) + \frac{2}{5} e^{-t} - \...
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1answer
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Find the frequency response if i have the magnitude response?

if i have the transfer function of magnitude response is there a method that i could calculate the frequency response? For example the transfer function of the magnitude response is: $ 3db \pm 3....
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1answer
121 views

Z-domain transfer function question

For the difference equation below: $y(k)=1/2{x(k)+x(k-1)}$ How i can find he z-domain transfer function? Thanks.
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2answers
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Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
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1answer
7k views

Use Butterworth and Chebychev filters

I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters. I'm developing in C++ with Qt, and I'm looking for algorithms ...
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1answer
384 views

Algorithm to estimate coherence when measuring a transfer function with a swept sine

I use a swept sine to measure a transfer function, multiplying the reponse by the in phase and quadrature excitation to get a complex response at each frequency. Can you suggest an enhancement to this ...
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2answers
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How to find poles of transfer function by looking at the step response?

How to find poles of transfer function by looking at the step response? Given a step response graph like such: How would I find the sketch for its poles on the complex plane? The only thing I can ...
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How do optical illusions work (photo mosaic) from a signal processing perspective?

Hello fellow investigators I have two question about optical illusions 1) A photo mosaic is something like this: What are the signal processing principles behind our eye merging the many tiny ...
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1answer
922 views

Amplitude vs Frequency Response

Consider the simple first-order low pass filter, described by $\tau \frac{d \mathcal{O}}{dt} + \mathcal{O}(t)=\mathcal{I}(t)$ Considered as a linear system (ie $\mathcal{L} \mathcal{O} = \mathcal{I}$...
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How to estimate a transfer function from a magnitude-only frequency response?

Given an arbitrary frequency response, what signal processing methods might exist that could guess, estimate or determine a transfer function (pole and zero constellation) which gives a "reasonably ...
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What do we know about the transfer function away from its zeros?

So lets say I have a transfer function for an FIR filter $H(z) = (z-a)...(z-n)$ where $a,...,n$ are points along the unit circle. But what about other points along the unit circle that correspond to ...
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1answer
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How to deal with a negative pole (unstable) in the pre-filter of a control system?

So while answering how to design a PI controller for a first order time delayed system (Question Here ) Here is the closed loop equation to a control system: $$ G_C(s) = \frac{\frac{K}{T}(1-sT)(s)...
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3answers
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Anti-causal systems

If Anti-causal systems are defined as those whose output depends solely upon future inputs.(Is this definition correct as I understand) So i see that $y[n] = x[n+2]$ ; is anticausal system How is a ...
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1answer
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How to find frequency response, stability, and causality of a linear system?

I have the following transfer function: $$H(s)=\frac{s}{(s+1)(s+2)}$$ How can I find the gain and phase response of the above system? I know the first step has something to do with substituting $s = ...
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What is the relation between the PSDs of filter input and output called? $R_Y = |H|^2R_X$

If a wide-sense stationary signal $X$ is fed to an LTI filter with the transfer function $H$, the power spectral density (PSD) of the output $Y$ can be expressed as: $$R_Y(f) = \left|H(f)\right|^2R_X(...
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Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...